Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009Simulation of the dynamic behaviour ofsteam turbines with ModelicaJuergen Birnbauma, Markus Joeckerb, Kilian Linka, Robert Pitz-Paalc, Franziska Tonia, GertaZimmerdaSiemens AG, Energy Sector, Erlangen, GermanybSiemens AG, Energy Sector, Finspång, SwedencGerman Aerospace Center, Institute of Technical Thermodynamics, Cologne, GermanydSiemens AG, Energy Sector, Muelheim, Germanyjuergen.firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,email@example.com, firstname.lastname@example.org, email@example.comAbstractSteam turbine technology is one of the leading technologies used in electricity production since morethan one hundred years. In recent time requirementsfor steam turbines have been changing slowly. Steamturbines are not longer used in power plants withhigh operation times and a high full load share only,but are also implemented in combined cycle powerplants or solar thermal power plants. This type ofplants requires good dynamic behavior of the steamturbine due to fast and frequent start ups and dailycycling.To optimize the performance of this kind ofpower plants and their components it is necessary tosimulate and analyze their dynamic behavior. Therefore, a general model approach for steam turbineswithin Modelica has been developed. This modelapproach is based on a general model, which can beadjusted to the necessary model depth as described inthis paper.Steam turbines in a solar thermal power plantwith direct steam generation must fulfill special requirements regarding their dynamic behavior. Hence,this model is applied as an example to explain thebehavior of an industrial steam turbine used in suchplants. Furthermore, this paper shows first results ofsimulations with turbine models. To validate themodel, the results are compared with results from theSiemens internal steady state calculation tool. Sinceresults stay within the estimated accuracy, the modelapproach can be used for further calculations.The dynamic behavior of the turbine is analyzedby using typical solar irradiance disturbances. Thisanalysis shows that no critical operation points occurwithin the turbine.Keywords: solar thermal power plant, dynamic turbine behavior, turbine modeling The Modelica Association, 20091IntroductionSteam turbines are typically used in different typesof power plants (e.g. fossil fired steam power plants,nuclear power plants, combined cycle power plants,solar thermal or biomass power plants) with differentrequirements regarding their dynamic behavior.Generally, a fossil fired steam power plant is operating more than 7000h a year with the rated poweroutput. Therefore, the dynamic behavior of the steamturbine is not essential for this kind of plants. Combined cycle power plants normally operate in middleload, hence the dynamic behavior of the steam turbine is of main importance for the start-up procedure. This aspect gained even more significancesince, due to the new grid requirements arising fromrenewable electricity generation, combined cyclepower plants are also used for peak load supply.The value of the dynamic behavior of steam turbines in a solar thermal power plant has been evenrising, since daily cycling, fast start-up behavior andgood transient behavior have become essential requirements. The dynamic behavior of the solar fieldand of the power block, especially the steam turbineand their interaction to bring solar thermal powerplants with direct steam generation into the market,are questions still to be answered. As an appropriatesolution, the layout of such a plant has been analyzedand optimized in a first step as described in  and. Further steps will be a dynamic analysis of thesolar field, of the turbine itself and their interactions.Parts of this analysis are already done and describedin . This paper addresses the modeling of such asteam turbine and provides a first analysis of its dynamic behavior.702DOI: 10.3384/ecp09430055
Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 200923.1Plant configurationThe basic layout of the analyzed solar thermal powerplant with direct steam generation is shown in figure1. It consists of a solar field, the power block basedon a Rankine-cycle and an optional thermal storagesystem.Modeling approachSteam turbines consist of different components,which are casing and shaft with the blading. Depending on the question to answer, the steam turbine hasto be modeled with a certain level of detail. Therefore, the model has been designed in a way that allows to simulate a single blading group as well as theturbine as a whole.The basic model, shown in figure 2, has beenbuilt-on a turbine section, an inlet and outlet volumeand the flange. The masses for the casing and theshaft are considered in corresponding wall models.figure 1: 50MWel parabolic trough power plant withdirect steam generationDuring the ITES project different power plantconfigurations have been designed . One of theseconfigurations, a plant layout for 50MWel with mainsteam parameters of 500 C and 110bar, has beenchosen for the modeling of the steam turbine and theanalysis of its dynamic behavior.The solar field is divided into four subfields, eachwith an evaporator and a superheater section, and isoperated in recirculation mode.  provides a detailed description of the solar field layout. The powerblock contains a steam turbine, which is divided intoa Hp- and a Lp- turbine, a feed water preheater section with six preheaters, the feed water pumps, thefeed water tank and a wet cooling tower. The steambetween the turbines is reheated again through asteam-steam reheater with condensation. This studydoes not focus on the optional thermal storage system which will, therefore, not be explained withinthis paper.3ModelingA general model has been developed to show thedynamic behavior of a “solar” steam turbine. Thisgeneral model can be adjusted to different turbinetypes and the necessary model depth. In this example, the “solar” steam turbine for the above describedplant layout is modeled within Modelica. The validation of the model approach is done through a comparison of the simulation results of this model withresults from stationary calculations by a Siemensinhouse tool. The Modelica Association, 2009figure 2: basic steam turbine modelThe mass flow through the turbine section is calculated by using Stodola’s law . Heat transfer between the steam and the casing respectively the shaftis calculated at the inlet volume. The level of detailfor the basic model is predefined depending on theinitial values for pressure and enthalpy and the geometric inputs (e.g. one basic model to model the Hpturbine).3.2Modeling of a “solar” steam turbineFigure 1 shows a schematic drawing of a parabolictrough power plant. However, to analyze the dynamic behavior of the steam turbine, it is not necessary to simulate the whole power plant as long asreasonable data for disturbances at the boundaries isavailable.Since enough data for disturbances around the“solar” turbine had been available, reasonableboundaries have been chosen (figure 3). The solar703
Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009field input and the mass flow at the extractions havebeen chosen as boundary conditions for the Hpturbine. Similar boundary conditions have been selected for the Lp-turbine, where, additionally, thecondenser backpressure has been selected. The massflow at the condensate side of the reheater is suitableas reheater boundary condition.figure 3: reasonable boundaries for the turbine modelDue to the chosen boundary conditions a reasonable design for the turbine model has to be appliedwhich is dividing each turbine into different sections.Each of these sections is described by the generalmodel. Three sections have been selected for the Hpturbine and five sections for the Lp-turbine. Eachsection is defined from turbine inlet respectively turbine extraction to the following turbine extraction.Figure 4 shows the overall turbine model and thedivision of the Hp-turbine into the three suitable sections.3.3Validation of the modelIn order to validate this model, results of the stationary calculations by the internal Siemens tool havebeen recalculated with Dymola/Modelica. Typically,load cases from 100% load down to 40% load insteps of 20% are calculated for this analysis. Theresults for these load cases of both tools were compared at the inlet of the different turbine sections andthe outlet of the Lp-turbine.The relative failure in the calculated mass flowthrough each turbine section is within 1.3% and –0.1%; for the enthalpy it is within 0.3% and -0.2%for all calculated load cases. Regarding pressure calculation, the relative failure stays within the samerange except for the Lp-turbine inlet, leading to afailure in the pressure calculation in every modeledsection of the Lp-turbine. Within those, the relativefailure varies over all load cases between 6.5% and-0.1%.This failure occurs from different calculationmethods used for the calculation of the pressure lossover the reheater within the tools. In the Dymola/Modelica model the pressure loss over the reheater is calculated according to a given geometry.In contrast, within the Siemens internal calculationtool the pressure loss in part load is calculated withan approximation considering the design pressureloss, the design mass flow and the actual mass flow.Exemplary the results for the 80% load case isshown in table 1.table 1: Comparison of the calculation results for80% load (turbine with reheat)figure 4: Overall turbine model and division of theHp-turbine into suitable turbine sections The Modelica Association, 2009rel. Failurep in %h in %mflow in %Hp-inlet1. extraction2. extractionLp-inlet3. extraction4. extraction5. extraction6. 0320.677A comparison of the pressure failure calculationwith the failure calculations of the enthalpy and themass flow shows a relatively high difference between the calculated pressure in Modelica and theSiemens inhouse tool. Due to this significant difference, a turbine model without reheater has been analyzed in the same way as described above.704
Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009The relative failure of the mass flow and the enthalpy calculation were in the same range as the relative failure calculated for these properties for theturbine design that has been analyzed first. The relative failure of the pressure calculation over the Lpturbine decreased to values between 0.1% and -1%.Hence, the different calculation methods used forpressure loss over the reheater could be determinedas the cause for the relatively high failure in pressurecalculation (table 2).table 2: Comparison of the calculation results for80% load (turbine without reheat)rel. Failurep in %h in %mflow in %Hp-inlet1. extraction2. extractionLp-inlet3. extraction4. extraction5. extraction6. et-0.0840.0720.001figure 5: typical irradiance disturbance and the corresponding solar field behaviorTo analyze the simulated dynamic behavior of theturbine the standard specification for steam turbinesIEC 60045-1 is used .4.1Taking into account the different calculationmethods for the pressure loss of the reheater, thecomparison of results between the two calculationtools shows a very good accuracy of the results. Theturbine model within Dymola/Modelica can, therefore, be used for further calculations. However, itshould be kept in mind, that the pressure loss calculation of any component used within the turbinemodel must first be analyzed separately.4Steam temperature limitsLooking at the steam temperature behavior of themodeled Hp- and Lp-turbine sections one can clearlysee that the temperature disturbance is softened overthe turbine especially over the reheater (figure 6).This behavior occurrs due to the thermal inertia ofthe turbine and the reheater. Therefore, the steamtemperature limits are analyzed only for the Hpturbine inlet, where the highest temperature stressoccurs.Simulation of the dynamic behavior of a “solar” steam turbineThe simulation of the dynamic behavior of the turbine is done for typical solar disturbances. Thesedisturbances are resulting in main steam parameterdisturbances. Within the ITES-Project, the GermanAerospace Center (DLR) is simulating the dynamicbehavior of the solar field for such power plants .The solar field outlet data (mass flow, temperature,enthalpy), calculated by the DLR, are used as inputdata for a simulation of the dynamic behavior of thesteam turbine. The typical disturbance used for thisanalysis is a step disturbance in the solar radiationfrom 550W/m² down to 275W/m² over 600s (figure5). The Modelica Association, 2009705figure 6: steam temperature behavior simulated fordifferent modeled turbine sections
Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009figure 7: excess steam temperature at the first modeled Hp-sectionfigure 8: temperature difference between steam andcasing respectively shaft at first Hp-sectionA detailed analysis at the Hp-inlet shows thattemperature limits of the turbine are significantlyovershot (figure 7). The temperature limits 8K and 14K over rated temperature must be analyzed on ayearly basis, as done in , to establish, whether thespecified limits have been exceeded. The temperature limit of 28K is an absolute temperature limit.Overshooting this temperature limit will normallylead to a turbine trip influencing the steady electricity production, or reducing the expected lifetime ofthe turbine. As this limit has been exceeded for 5minutes, this would already lead to a trip or significant reduction in turbine lifetime.4.2Temperature differences between steamand casing respectively shaftAnother limit of the turbine, which has to be fulfilledin operation, is the temperature difference betweensteam and casing respectively shaft. In case the temperature difference is exceeding a certain degree, thethermal stresses within the turbine will get too highwhich will lead to a reduced lifetime of the turbine.The temperature difference between the steamand the shaft respectively casing is analyzed for theHp-inlet (figure 8) and the Lp-inlet (figure 9). Thedifference between the steam temperature and theshaft temperature of the first Hp-section as well asthe first Lp-section is below 0.4K. Like the shafttemperature, the temperature of the casing at the firstHp-section is nearly exactly following the steamtemperature. The temperature of the first Lp-sectioncasing for the analyzed disturbance is 5.4K lowerthan the steam temperature. The bigger mass of theLp-casing compared to the Hp-casing and the shaftsof the Hp- and Lp-turbines mainly cause this temperature difference. However, all analyzed temperature differences are well below their specified limits. The Modelica Association, 2009figure 9: temperature difference between steam andcasing respectively shaft at first Lp-section4.3Temperature distribution within the casingAnother characteristic for the dynamic behavior ofthe turbine is the temperature distribution in the casing. If the temperature gradient from the inner to theouter wall of the casing is too big, the thermal stresswithin the casing will exceed its limits, which willagain lead to a reduced lifetime of the turbine.Since the highest temperature stress has beensimulated for the first turbine section, the temperature distribution within the casing is analyzed for thissection. Therefore, the casing is divided into six layers each with the same mass from the inner to theouter wall.Figure 10 shows the maximal temperature difference of 34K between the inner and the outer wall.The maximal tolerable temperature gradient, previously determined during first approximations, is 50K. The determined temperature gradient stays,therefore, well within these limits.706
Proceedings 7th Modelica Conference, Como, Italy, Sep. 20-22, 2009AcknowledgementsThe authors would like to thank the German Ministryfor the Environment, Nature Conservation and Nuclear Safety for the financial support given to theITES project (contract No 16UM0064).Referencesfigure 10: temperature gradient within the casing ofthe first Hp-section (6 wall layers)4.4Pressure limitsThe standard specification of the pressure disturbances for steam turbines defines only maximalpressure limits . The main steam pressure for theanalyzed disturbance coming from the solar field isnever exceeding the rated pressure (figure 7). Sincein the solar field no overpressure has been simulatedit is not necessary to analyze the turbine regarding itspressure behavior.5ConclusionsThis paper presents a model approach for the simulation of the dynamic behavior of steam turbines. Forthe purposes of an industrial steam turbine within asolar thermal power plant with direct steam generation the model approach has been compared withstationary calculations for different load points. Thiscomparison revealed a very high accuracy of Dymola/Modelica simulations results, hence, this modelcan be used for further calculations.The analysis of the dynamic behavior of the turbine within a solar thermal power plant shows thatmost of the typical limits for steam turbines have notbeen exceeded. The limit, which in fact has been exceeded, is the absolute temperature limit at the Hpturbine inlet. One possibility to control the mainsteam temperature within its allowed limits is to optimize the solar field control strategy. Another possibility has been evaluated within the ITES-project,where a short time storage had been integrated intothe main steam path. The results of this analysis arepublished in . The Modelica Association, 2009707Birnbaum J., Eck M., et al. A Direct SteamGeneration Solar Power Plant with IntegratedThermal Storage. Las Vegas, USA: 14thBienial SolarPACES Symposium, 2008.Birnbaum J., Hirsch T., et al. A Concept forFuture Parabolic Trough Based Solar Thermal Power Plants. Berlin, Germany: 15th International Conference on the Properties ofWater and Steam, 2008.Birnbaum J., Feldhoff J., et al. Steam Temperature Stability in a Direct Steam Generation Solar Power Plant. Berlin, Germany:15th Bienial SolarPACES Symposium, 2009.Traupel W. Thermische Turbomaschinen II.,3. edition. Berlin, Heidelberg, New York:Springer Verlag, 1982.International Electronic Commission (IEC)Steam turbines – Part 1: Specifications, IEC60045-1. Geneva, 1991
firstname.lastname@example.org , email@example.com , firstname.lastname@example.org , email@example.com , firstname.lastname@example.org , email@example.com Abstract Steam turbine technology is one of the leading tech - nologies used in electricity production since
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